Internal energy Definition and 381 Threads

Consider the function ##U=U(T,L,N)##. $$dU=\left (\frac{\partial U}{\partial T}\right )_{L,N} dT+\left (\frac{\partial U}{\partial L}\right )_{T,N} dL+\left (\frac{\partial U}{\partial N}\right )_{T,L} dN$$ and define $$C_L\equiv\left (\frac{\partial U}{\partial T}\right )_{L,N}$$ By the...

This was the question This is my solution The problem arose after reading this post on PhysicsSE and this answer given So If I remember correct work done is ##-P_{ext}\Delta V## I don't understand why $$\Delta H=\Delta U+(5×4-1×10)L.atm$$ If that answer (the answer on the PSE post) is...

For this, They say internal energy is the sum of the all the mechanical energies of each particle in within the thermodynamic system, however, they then define internal energy differently using the average mechanical energy for all particles within the system (Pink equation). Does someone...

Since the system is doing no work, would it be just 4513 J? I don't think there is any other information to use

So the question goes like this: find change in internal energy in process 1->2 using diagram. And offered solutions a)-400J b)400J c)600J d)800J. First I found T1 and T2 using (P*V)/T=R and got T1=24K and T2=72K. Then I found n(number of moles) using PV=nRT and got n1=1mol, n2=1mol. Then I...

I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some part (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...

I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some point (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...

Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##. What is said is...

This is a thermodynamics question. A gas absorbs 10 000 J of heat , it releases 3000 J and does 2000 J of work. How much has the internal energy varied? So I did 10 000 - 3000 -2000 = 5000 J so internal energy decreases by 5000 J. But the correct answer is A) it increased by 5000 J . How ?

https://www.nature.com/articles/s41598-022-11093-z In this new 2 May 2022 publication, an experimental effort was made to measure directly the internal energy changes of non-ideal CO2, from the decrease in temperature as the liquid-gas expanded from one cylinder into two. With the empirical...

I believe I got the first part of this questions solved. For part b, we are asked to find the change in internal energy. We know ΔE=Q+W. The cylinder,gas and piston head are the system. The cylinder and piston head are well insulated, so there will be no head transfer, therefore Q=0. So now...

a) We use the definition of heat transfer in a gas at constant volume: Q = n*C_v*delta_T = (0.01 mol)(12.47 J/mol*K)(40 K) = 4.99 J b) We use the definition of heat transfer in a gas at constant pressure: Q = n*C_p*delta_T = (0.01 mol)(12.47 J/mol*K)(40 K) = 8.31 J c) In both processes delta_U...

ΔQ=mC(T3-T1) But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be. Feeling so confused

If we look at system at constant temperature and volume which is galvanic cell, first law of thermodynamics states: $$ dU = dQ + dW' $$ Where W' is electrical work done by galvanic cell and Q is heat exchanged with surroundings. As far as I know electrical work is work done by electric field...

Well, internal energy is the sum of the kinetic and potential energies of all the molecules within a given mass of a substance; this energy is associated with the random, disordered motion of the molecules. An example of internal energy is compressed gases; since gases occupy the total volume...

Is the purpose of the 0th, 1st & 2nd Laws of Thermodynamics simply to legitimate the thermodynamic properties of Temperature, Internal Energy & Entropy, respectively? It seems that all these laws really do is establish that these properties are valid thermodynamic state properties and the...

Am i right Is internal energy for engineering just the sum of energy stored with a system of a substance. which is only affect by heat and work coming out of the system

Summary:: How internal energy changes in a acclerated cabin. There are two tourus shaped insulated closed pipes containing equal amounts of ideal gas under same conditions. B has a adiabatic partion wall. If both are to change angular velocity by w radians per second. How internal energies...

Hello, In thermodynamics, with systems being represented by gases (can liquids be also included?), the internal energy ##E_{int}## of a system represents the total kinetic energy + the total potential energy of the system: $$E_{int} = KE_{tot}+ PE_{tot}$$ The term ##KE_{tot}=Q## is also called...

I tried using U=3/2 NKbT, but i don't seem to get the correct answer..

The question is simply why i can't use ∂U/∂V = -P? (

I'm inclined to say no, but am by no means certain. The total kinetic energy of a system of particles is $$T = \sum_{i} \frac{1}{2} m_{i}\vec{v_i}\cdot\vec{v_i} = \frac{1}{2} m_{i}(\vec{v_{COM}} + \vec{v_{i}^{'}})^{2} = \frac{1}{2}M\vec{v_{COM}}^{2} + \frac{1}{2}\sum_{i} m_{i}...

Question: Solution manual: Is the solution manual correct or not? why does not contain heat transfer?

I assume this interaction is an explosive separation one, and as such, I thought the problem gave me the numbers to satisfy the second equation. I converted the 238 amu and 234 amu and plugged the results into the second equation of 0 = m1v1f + m2v2f. I got 0 = (3.95*10^-25kg)v1f + 3.88*10^-25kg...

I've come across some conflicting definitions and hoped someone more in-the-know could clarify a few points. The rest energy is the total energy of the system in its rest frame; I read about the following (approximate!) semi-empirical mass formula earlier, and if we multiplied this through by...

According to the first principle of thermodynamics: ΔU = W + Q Also noting that: W = -P⋅ΔV (Question: This P is the initial pressure or the final?) To find V2: (P1⋅V1) / T1 = (P2⋅V2) / T2 → Therefore, (P⋅V1) / T1 = [(P/5)⋅V2] / T2 → (P⋅V1) / T1 = (P⋅V2) / (5⋅T2) → V2 = (5⋅T2⋅V1) / T1...

I've worked out that half of the steam must condense (since the pressure of the steam needs to remain constant for the forces on the massless piston to balance). Also, if the total volume of the container is ##V##, the work done on the system equals ##\frac{P_{atm}V}{4}##. When half of the steam...

Why we do not considered the translational energy of the gases particles in the internal energy due to ordered motion but only due to random motion.

Homework Statement: A quantity of ideal gas initially at 20 atmospheres in a volume of 1 litre and a temperature of 300K suddenly expands and comes to equilibrium with a volume of50 litres and a pressure of 1 atmosphere. If the process is irreversible and involves the transfer of heat and work...

Hello, I'm doing some refreshers before going back to school. Stat mech is my shakiest and I'd appreciate some help on this problem. I know that for a single particle, the partition function will be $$Z = 1 + 2e^{-\beta\Delta} + 2e^{-4\beta\Delta}$$ and so its internal energy is $$\frac{1}{Z}...

Is there anybody who can advise wether the heat lost / gained during vaporisation, is best calculated from enthalpy, or from internal energy, in the steam tables? I am trying to establish the increase in the volume of milk when the temperature is raised by adding saturated steam at 1 bar (1...

Using (2) on (1) give ## dU = -dW##... (4) A.For expansion since the gas goes from ##(P_1, V_1, T_1)## to ##(P_2, V_2, T_2)##, does this imply ##T_1 \leq T_2 ##? B. If so, then ##W## for adiabatic expansion would be negative (using (3))? Using negative ##dW## in (4) gives us a positive result...

I’m having a mental block re. teaching internal energy. Here’s the issue: For ideal gas, internal energy is entirely kinetic energy. I explain to students this is because there are no interatomic forces of attraction. Now, a solid...internal energy is sum of kinetic energy and potential...

I have the definition of change in internal energy. $$ \Delta U = Q - W $$ I can get the work by $$ W = \int_{V_1}^{V_2} p dV = p \Delta V $$ however the pressure isn't constant so this won't do. ## W ## is work done by the gas and ## Q ## is amount of heat energy brought into the system. I'm...

Good day all ! I have a confusion regarding the use of the formula dU=CdT for computing internal energy for liquid or solid like for instance in this exercice We have an isothermal process so I thought that dU=0 so according to the first law of thermodynamics dQ=-dW (we want to calulate the...

Homework Statement Which statement about internal energy is correct? A. When two system have the same internal energy, they must be at the same temperature B. When the internal energy of a system is increased, its temperature always rises C. The internal energy of a system depends only on its...

My book states that Heat and work represent energy in transit. The state of the system undergoes a change after heat is supplied to it and before work is extracted from it because energy gets stored in it. My doubt is here that ,heat has been transferred to the system and it says heat is energy...

I have a plate capacitor with a given charge. It is then dipped in a dielectric fluid and I must determine which height the fluid reaches(all the necessary parameters are given). I can solve this problem if I make the following assumption: the polarization of the dielectric does not( or...

MODERATOR'S NOTE: I have been having difficulty explaining to this member the error in his algebraic development, in particular being cavalier in his attentiveness to proper algebraic manipulation of signs. I explained his error in post #7 (and the problems that could arise if he continues to...

Greetings! I've been brushing up on some thermodynamics recently and came across a perplexing sentence in my notes and text from undergrad. It says that for a combustion reaction, such as the combustion of heptane: C7H16 (l) + 11O2 (g) ---> 7CO2 (g) + 8H2O (l) That this process carried out at...

I'm watching a lecture introduction internal energy and in it, the lecturer states the following for some system: E_{internal} = E_{translational} + E_{vibrational} + E_{rotational} + E_{other} where ## E_{other} ## could be chemical energy, magnetic energy, electrostatic energy etc. Then...

Homework Statement Match the following Given : Processes do not include chemical reactions. Assume CP,m and CV,m are independent of temperature for given substance and consider only pressure-volume work in given all processes. Homework Equations ΔU = Q - W ΔH = ΔU +...

Homework Statement If water vapor is assumed to be a perfect gas, molar enthalpy change for vaporization of 1 mol of water at 1 bar and 100 C is 41 kJ/mol . Calculate the internal energy, when 1 mol of water is vaporized at 1 bar pressure and 100 C. Homework Equations $$\Delta U = \Delta H =...

I'm reading a book on thermal physics and the author says this: "In general, the internal energy will be a function of temperature and volume, so that we can write U =U(T,V) " How do we know this intuitively and how do we know that internal energy is not a function of pressure as well?

From what I understand, the molecules/atoms that make up an object are in constant, random motion. Do electromagnetic forces cause this motion or what is the cause of it? If so, why would net electromagnetic forces exist between "neutral" atoms?

Homework Statement Re-arranging the equations of potential (internal) energy in a monoatomic gas, i get this differential equation: \gamma (dV/V ) + (dP/P) = 0. where V is volume and P is pressure. I have to integrate it. Homework EquationsThe Attempt at a Solution I tried, but i wasnt able...

Homework Statement Homework Equations F= ma P= F/A The Attempt at a Solution a). Assuming the piston is in equilibrium, I'm applying Newton's second law F=ma=0 Equals zero because it is not moving Note: P=F/A which I rearrange to solve for the force for F= PA. This represents the...

Hello. I am starting to learn about thermodynamics. (i'm going to use lower case "d" for delta) Energy is neither created nor destroyed. So dU = 0 for the universe as a whole. If the universe is constantly expanding, then it must be doing work on the vacuum around it, right? So W is a...